论文标题
在加权分数Sobolev空间中平滑功能的密度
On density of smooth functions in weighted fractional Sobolev spaces
论文作者
论文摘要
我们证明，在重量的某些轻度条件下，在任意开放式的加权分数Sobolev空间中，平滑的$ c^\ infty $函数在加权分数sobolev空间中密集。我们还在某些内核定义的非加权空间中获得了一个相似的结果，类似于$ x \ mapsto | x |^{ - d-sp} $。人们可能认为结果是迈耶斯 - serrin定理的〜版本。
We prove that smooth $C^\infty$ functions are dense in weighted fractional Sobolev spaces on an arbitrary open set, under some mild conditions on the weight. We also obtain a~similar result in non-weighted spaces defined by some kernel similar to $x\mapsto |x|^{-d-sp}$. One may consider the results to be a~version of the Meyers--Serrin theorem.
